p-adic Numbers, p-adic Analysis, and Zeta-Functions: Graduate Texts in Mathematics, cartea 58
Autor Neal Koblitzen Limba Engleză Hardback – 23 iul 1984
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Specificații
ISBN-13: 9780387960173
ISBN-10: 0387960171
Pagini: 153
Ilustrații: XII, 153 p.
Dimensiuni: 155 x 235 x 15 mm
Greutate: 0.48 kg
Ediția:2nd ed. 1984
Editura: Springer
Colecția Springer
Seria Graduate Texts in Mathematics
Locul publicării:New York, NY, United States
ISBN-10: 0387960171
Pagini: 153
Ilustrații: XII, 153 p.
Dimensiuni: 155 x 235 x 15 mm
Greutate: 0.48 kg
Ediția:2nd ed. 1984
Editura: Springer
Colecția Springer
Seria Graduate Texts in Mathematics
Locul publicării:New York, NY, United States
Public țintă
GraduateCuprins
I p-adic numbers.- 1. Basic concepts.- 2. Metrics on the rational numbers.- Exercises.- 3. Review of building up the complex numbers.- 4. The field of p-adic numbers.- 5. Arithmetic in ?p.- Exercises.- II p-adic interpolation of the Riemann zeta-function.- 1. A formula for ?(2k).- 2. p-adic interpolation of the function f(s) = as.- Exercises.- 3. p-adic distributions.- Exercises.- 4. Bernoulli distributions.- 5. Measures and integration.- Exercises.- 6. The p-adic ?-function as a Mellin-Mazur transform.- 7. A brief survey (no proofs).- Exercises.- III Building up ?.- 1. Finite fields.- Exercises.- 2. Extension of norms.- Exercises.- 3. The algebraic closure of ?p.- 4. ?.- Exercises.- IV p-adic power series.- 1. Elementary functions.- Exercises.- 2. The logarithm, gamma and Artin-Hasse exponential functions.- Exercises.- 3. Newton polygons for polynomials.- 4. Newton polygons for power series.- Exercises.- V Rationality of the zeta-function of a set of equations over a finite field.- 1. Hypersurfaces and their zeta-functions.- Exercises.- 2. Characters and their lifting.- 3. A linear map on the vector space of power series.- 4. p-adic analytic expression for the zeta-function.- Exercises.- 5. The end of the proof.- Answers and Hints for the Exercises.
Recenzii
From the reviews of the second edition:
“In the second edition of this text, Koblitz presents a wide-ranging introduction to the theory of p-adic numbers and functions. … there are some really nice exercises that allow the reader to explore the material. … And with the exercises, the book would make a good textbook for a graduate course, provided the students have a decent background in analysis and number theory.” (Donald L. Vestal, The Mathematical Association of America, April, 2011)
“In the second edition of this text, Koblitz presents a wide-ranging introduction to the theory of p-adic numbers and functions. … there are some really nice exercises that allow the reader to explore the material. … And with the exercises, the book would make a good textbook for a graduate course, provided the students have a decent background in analysis and number theory.” (Donald L. Vestal, The Mathematical Association of America, April, 2011)